<title>Numerical investigation of the Knudsen-layer, appearing in the laser-induced evaporation of metals</title>

Abstract

The non-equilibrium evaporation of metals is increasingly important in recent applications of high intensity power sources such as lasers, electron beams and arc heated plasmas. Powerful jets of evaporated metal arise when cw-lasers or pulsed laser beams are used, especially in surface processing, ablation and sublimation cutting. An exact understanding of the physical conditions in this evaporation jet is essential to control the ablation rate and minimize the energy loss due to evaporation by adjustment of the external process parameters. The ablation jet is maintained by an appropriate supply of newly evaporated particles and in effect sets the boundary conditions for the hydrodynamic or plasma regime that arises. Exact knowledge concerning the metallic vapour that constitutes the plasma which arises in a wide variety of material processing techniques with a high intensity beam allows to predict the ignition behaviour of the plasma vapour. This is a particular advantage since the presence of the plasma can totally change the physical behaviour of the process. In high intensity beam welding processes a narrow keyhole appears filled with metallic vapour whose behaviour does not depart too strongly from equilibrium. The plasma which is detected in the keyhole is important for the energy transfer from the incident beam to the workpiece1, so that in this case the physical conditions in the vapour are of special interest, as they determine the development of the plasma. When a metal surface is heated to a temperature close to the boiling point of the material of which it is composed, a jet of evaporated material originates at the metal surface. Depending on the surface temperature and the external pressure, the evaporation process ranges from a steady state of thermodynamic equilibrium which describes a vapour with constant spatial density and temperature, and no significant net motion, to one involving a strong non-equilibrium process with a velocity up to the local speed of sound. In all but the equilibrium case, however, a thin surface layer, known as the Knudsen layer, forms in the vapour. The transition from a non-equilibrium velocity distribution at the metal surface to a local Maxwell-Boltzmann distribution some few mean free paths above the metal surface occurs in this layer. This non-equilibrium regime is described by Boltzmann's equation which is solved here in the BGK approximation. This is achieved by employing an iteration algorithm for the solution of an equivalent integral equation with suitable boundary conditions. The temperature, density and velocity either in or behind the Knudsen layer are derived together with the velocity distribution function everywhere in the layer.